Finite Group Databasebeta

← #20242698

Subgroups — #20242698

Order 6016.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689877C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic, complemented
3#15689515C211yesmaximal, characteristic
4#15688865C211yesmaximal, characteristic, complemented
5#15688864C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic
7C47×#501C211yesmaximal, characteristic, complemented
8C2×#10625337—21no—
9C2×#10625336—21no—
10#13094023—21no—
11#13094019—21no—
12#13094019—21no—
13#13094016C2211yescharacteristic
14#13094012C2211yescharacteristic
15#13094009—21no—
16#13094004—21no—
17#13094002—21no—
18#13093957—21no—
19#13093955—21no—
20#13093935C2211yescharacteristic
21#13093935C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#125×C47C2211yescharacteristic
24#107×C47—21no—
25#106×C47—21no—
26#97×C47C2211yescharacteristic
27C2×Q8×C47—21no—
28C2×D188D411yescharacteristic
29C2×C4×D47—21no—
30C2×Dic94—21no—
31C2×Dic94D411yescharacteristic
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C4⋊C4×C47D411yescharacteristic
39C42×C47C2311yescharacteristic
40#10625337—42no—
41#10625336—42no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47D411yescharacteristic
49C4⋊Dic47D411yescharacteristic
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53C4×Dic47—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C22×D47—21no—
57Q8×C47—41no—
58Q8×C47—41no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—41no—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68D188—41no—
69C4×D47—81no—
70Dic94—41no—
71Dic94—81no—
72C8×C47—22no—
73C47⋊C8—22no—
74C47⋊C8—22no—
75C22×C47#12011yescharacteristic
76C2×D47—41no—
77C2×D47—41no—
78C2×D47—41no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—41no—
83C4×C47—41no—
84C4×C47—81no—
85Dic47—41no—
86Dic47—41no—
87Dic47—41no—
88#1660—471nomaximal, Sylow
89C2×C47#45311yescharacteristic
90C2×C47#45611yescharacteristic
91C2×C47#45611yescharacteristic
92D47—81no—
93#563—471no—
94#501—471no—
95#501D4711yescharacteristic, complemented
96#497—471no—
97#330—471no—
98#330—471no—
99#329—471no—
100C47#166011yescharacteristic, complemented, Sylow
101C2×Q16—941no—
102C2×SD16—941no—
103C4⋊Q8—941no—
104C4⋊Q8C2×D4711yescharacteristic
105#126—941no—
106#126—941no—
107#125—471no—
108#125C2×D4711yescharacteristic
109#124—471no—
110#123—941no—
111C22⋊Q8—941no—
112C22⋊Q8—941no—
113#107—21no—
114#107—941no—
115#106—21no—
116#106—941no—
117#97—471no—
118#97—471no—
119#97C2×D4711yescharacteristic
120C2×Q8—21no—
121C2×Q8—471no—
122C2×Q8—941no—
123C2×D4—471no—
124C22×C4—941no—
125Q16—1882no—
126SD16—1882no—
127C2×C8—21no—
128C2×C8—941no—
129C2×C8—941no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—471no—
135C4⋊C4—471no—
136C4⋊C4—941no—
137C4⋊C4—941no—
138C4⋊C4—941no—
139C4⋊C4—941no—
140C4⋊C4C22⋊D4711yescharacteristic
141C4⋊C4C22⋊D4711yescharacteristic
142C22⋊C4—941no—
143C22⋊C4—941no—
144C22⋊C4—941no—
145C22⋊C4—941no—
146C22⋊C4—941no—
147C42—941no—
148C42C22×D4711yescharacteristic
149C23—941no—
150Q8—41no—
151Q8—41no—
152Q8—3761no—
153Q8—1881no—
154D4—1881no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—941no—
159C2×C4—941no—
160C2×C4—941no—
161C2×C4—3761no—
162C2×C4D4×D4711yescharacteristic
163C2×C4D4×D4711yescharacteristic
164C2×C4C2×C22⋊D4711yescharacteristic
165C8—22no—
166C8—942no—
167C8—942no—
168C22—1881no—
169C22—1881no—
170C22—1881no—
171C22#1309399211yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—1881no—
179C4—1881no—
180C4—1881no—
181C2—3761no—
182C2#1568928911yescharacteristic
183C2#1568930411yescharacteristic
184C2#1568930511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#501C2
socleC22×C47#120
hypercenter#501D47
hypocenterC47#1660
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #15689529C2semidirect
4. #15688865C2semidirect
5. #15688864C2semidirect
7. C47×#501C2semidirect
95. #501D47semidirect
100. C47#1660semidirect